I had coworkers (and people up my chain of command) that did/do this. The thing all those people had/have in common is that they came from the military. So I always took it as a military thing. Curious if that particular coworker had a military background.
Creating a voicemail greeting might not be fun, but with the scripts I’ve shared, you should have an easier time. No need to practice time and time again — simply plug in your name, company title, and other details, then read it out loud to your phone’s voicemail greeting recorder. With a professional greeting, you’ll continue nurturing prospects even if you don’t pick up the phone.

“Hi, I’m Troy McClure!” We’re not sure who wrote the original Troy McClure out of office message, but this version by Paul Sokol of Infusionsoft is a real gem.
I usually put my boss in my OOO, because if something is so urgent that it needs to be delegated RIGHT NOW then it’s urgent enough that my boss should know about it, and he’s also in the best position to know who on the team to delegate it to based on everyone’s workloads and what can be dropped. But the most likely result is that whoever is emailing me either waits for me to get back because it’s not that urgent or goes to the next/backup person based on our central documentation about who to contact for particular issues.